Williams was absent for most of Tasmania's second innings which saw them crumble to 244 after being set a daunting task by Western Australia.
The home team enjoyed a 220-run lead on the first innings after declaring at 478-9 in reply to Tasmania's first innings tally of 258.
Western Australian captain Mike Hussey had set up the lead with a knock of 210 while Brad Hogg led the bowling, devastating Tasmania with second innings figures of 6-44.
Needing just 225 runs to win on Wednesday, Western Australia reached the target after 6.4 overs with the loss of only Ryan Campbell for 10.
Williams is expected to be out of action for three to four weeks after tearing a muscle above his right knee.